Problem: Simplify; express your answer in exponential form. Assume $y\neq 0, n\neq 0$. $\dfrac{{(y^{4})^{-3}}}{{(y^{-1}n^{4})^{-4}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${y^{4}}$ to the exponent ${-3}$ . Now ${4 \times -3 = -12}$ , so ${(y^{4})^{-3} = y^{-12}}$ In the denominator, we can use the distributive property of exponents. ${(y^{-1}n^{4})^{-4} = (y^{-1})^{-4}(n^{4})^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y^{4})^{-3}}}{{(y^{-1}n^{4})^{-4}}} = \dfrac{{y^{-12}}}{{y^{4}n^{-16}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{-12}}}{{y^{4}n^{-16}}} = \dfrac{{y^{-12}}}{{y^{4}}} \cdot \dfrac{{1}}{{n^{-16}}} = y^{{-12} - {4}} \cdot n^{- {(-16)}} = y^{-16}n^{16}$.